Standard and Function Form of Linear Equation

1. Finding the Rule of a Line

2. A straight line always follows the RULE
y = mx + b
m  is the slope
b  is the y-intercept
Where;
y  is a y-coordinate
x  is an x-coordinate

5. Standard to Function
• 2x + y = 5 2y = 5x -6
• -4x + y = 8 x -2y = 10
5

6. Steps to solving Linear Functions
1. Determine x (independent) and y (dependant)
Hint: Words
2. Determine a (slope or rate) and b (y-int or initital value)
Hint: Values
3. Write the rule of the function if the form y=ax+b
Example: y = 2x + 10
4. Solve the question. Can now plug any value in for
x and solve y or plug any value for y and solve x.

7. x y
x y
x y
x y
x y
-2 -1
0 0
2 1
y =
1
2
x
x y
-2 -3
0 -2
2 -1
y=
1
2
x−2
y=
1
2
x−4
x y
-2 -5
0 -4
2 -3
y=
1
2
x+2
x y
-2 1
0 2
2 3
2. Changing the y-intercept (b)
b translates the line vertically (up or down).

8. Steps to Finding the RULE given 2 points
Step 1: Find the slope using a= y2-y1
x2-x1
Step 2: Find the y-intercept (b) by plugging
an (x,y) coordinate into y=ax+b
Step 3: State the final equation.
Sketch to verify your answer

9. Step 3: Final equation
Find the equation of the line going through (-6,5) & (-4, 6)
Step 1: Find a
a =
x2-x1
y2-y1
=(6) - (5)
(-4) - (-6)
a =
1
2
Step 2: Find b using (-6,5)
y=ax + b
(5) =
1
2
(-6) + b
(5) = -3 + b
+3 +3
b = 8
y=1
2
x + 8

10. Step 3: Final equation
Find the equation of the line going through (-2,6) & (1, 3)
Step 1: Find a
a =
x2-x1
y2-y1
=(3) - (6)
(1) - (-2)
a =
-3
3
Step 2: Find b using (1,3)
y=ax + b
(3) =-1(1) + b
(3) = -1 + b
+1 +1
4 = b
y=-1x + 4
a = -1